DETROIT - Red Sox president Larry Lucchino said on Friday the team would be willing to add to the payroll to improve the pitching staff.

In an appearance on MLB Network Radio, Lucchino said the team would be over the luxury tax threshold regardless.

“I don’t think there’s any question about that. We’ve been above the threshold the last couple of years,’’ he said.

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“Our goal is to field a team with more homegrown players, fewer free agents, and to have a more manageable payroll down the road. But if you’re asking about this year, we understand that each year has to be taken on its own and this year our payroll is going to be, I’d hate to make a guess, but it’ll be well over the $178 million dollar threshold.’’

Roy Oswalt is unsigned, although he says he plans to join a contender. The 34-year-old righthander was 9-10 with a 3.69 earned run average in 23 starts for the Phillies last season.

Signing Oswalt would allow the Red Sox to shift Daniel Bard or Felix Doubront into the bullpen.

Lefthanded reliever Mike Gonzalez, who turns 34 in May, also is available. He appeared in 56 games for the Orioles and Rangers last season, holding lefthanded hitters to a .214 batting average.

But with lefthander Rich Hill close to beginning a minor league rehabilitation assignment, Gonzalez may not necessarily fill a need.

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Long term, Lucchino said, the Red Sox will look to get under the threshold. Under the terms of the new collective bargaining agreement, large-market teams under the threshold can get a return on some luxury-tax payments.

As a further benefit, getting under the threshold once wipes clean the penalties for having been over in previous seasons. So getting under the threshold in 2013, as an example, would allow the Red Sox to go over in 2014 without being taxed as heavily.

“It’s important to us to get under the threshold when we can, depending on when the circumstances will allow us to do so,’’ Lucchino said. “Our first and fundamental obligation to our fans, the first and fundamental obligation of ownership, is to field a team that’s worthy of the fans’ support. I think our track record over the past 10 years demonstrates that we honor that obligation and we will continue to honor that obligation.

“But that doesn’t necessarily, by definition, mean that you must be millions and millions of dollars over the tax threshold. There are several teams out there that have worthy teams that are sources of pride for their community, that are well under the threshold.

“Ultimately we’d love to field the team we need to field with fewer dollars, if that’s possible at the major league level. We’re always going to invest a tremendous amount of money into scouting and player development because that’s the secret.’’

Beckett next

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Josh Beckett, who starts against the Tigers Saturday, is 3-2 with a 2.50 earned run average in his career against Detroit and has allowed only three earned runs in 20 2/3 innings at Comerica Park.

The nine players who started for Detroit on Thursday are 16 of 70 (.229) against Beckett with one home run, that coming from Prince Fielder.

Schilling retreats

Curt Schilling is backing off his relentless criticism of Bobby Valentine.

“The problem here is this has been positioned as me against Bobby V and I feel bad,’’ Schilling told ESPN Boston Radio.

“I disagreed with some things that he did. I stated my opinion in disagreeing. People act like I am openly rooting against him and nothing can be further from the truth. I like Bobby, I think he’s a very smart baseball guy. I disagree with some of the stuff that he did, that’s what I get paid to do. I gave my opinion and if he disagrees with it that’s his prerogative, that’s fine.’’

Valentine has been dismissive of Schilling, saying he considers the source of the criticism and that he has better things to do with his time than worry about the former major league pitcher and ESPN analyst. Valentine also referred to the comments as “silly.’’

Schilling, a longtime supporter of former Red Sox manager Terry Francona, criticized Valentine for his handling of Daniel Bard, a notion Bard disagreed with. Schilling also claimed to have spoken to players who were unhappy with Valentine, a comment Beckett mocked.

Even Lucchino came out against Schilling, saying the Red Sox are fortunate he has no influence on decisions.

Schilling persisted with his attacks Thursday. He took to Twitter and compared the Red Sox to the Titanic because Valentine agreed to appear on a radio show in New York.

“The Michael Kay Show’’ is on ESPN Radio, putting Schilling in the position of disparaging his employer.

Schilling claimed he was “dared’’ to write that Tweet.

“I probably shouldn’t have. It was all said in fun and jest . . . We were having fun and joking around and I tweeted it. I got a rash of crap for it, by the way,’’ he said.

Carlson slowed

Lefthander Jesse Carlson, who did not pitch last season because of a shoulder injury, is continuing to work out in Fort Myers, Fla., with the hope of joining a minor league team this season.

Carlson got in five games during spring training.

“We hadn’t seen quite the same stuff, so we decided to slow him down and build some arm strength,’’ general manager Ben Cherington said.

Carlson appeared in 73 games for the Blue Jays in 2009 before the onset of his shoulder issues.